The identification of effect modifiers will likely require prior background knowledge and substantive domain expertise. Bias-variance trade-offs are also important. Failing to include an influential effect modifier in \(\mathbf {z}\) , whether in imbalance or not, leads to bias in \(S=2\)  [1]}, [2]}, [3]}. On the other hand, the inclusion of covariates that are not effect modifiers reduces overlap, thereby increasing the chance of extreme weights. This decreases precision without improving the potential for bias reduction [4]}, [5]}, even if the covariates are strongly imbalanced across studies. That is, even if they predict or are associated to trial assignment.
